Theory of Music #2

In the previous lesson
we've learnt which pitches are used in music and what they are
called. Today we will learn to draw them on the staff. The author of
this text believes that staff has its flaws in registering music.
Why? A couple of reasons can be thought of:

the lengths of notes
are not intuitive and legible at first, i.e., especially at the
beginning of learning, it's hard to see how identically sized black
dots translate into rhythm. Today we would call it weak
user-experience.

Music markup becomes
incredibly complicated when we try to convey the “feeling” of a
piece (that is, small deviations from rhythm that make the song not
sound like a karaoke track).

Not every musical instrument maps well onto
musical score. A good proof of this is the popularity of tablatures
among guitarists.

It is easy to criticize, meanwhile we live in a world
where there is no alternative, commonly respected notation. If it
wasn't the case fact we probably wouldn't bother you with sheet
music!

Of course we need to remember that the knowledge
of musical score is not mandatory. Notes are only a way of
communication among musicians, so if we want to create solely for our
personal needs, we will be able to do without them (what, in fact, is
practiced by many famous artists). You need to know the rules of
harmony, but you can learn them with no notes involved.

Each note on the staff stands for one tone. Vertical
position of the note (that is top-bottom) determines the pitch of
sound (that is, frequency). The higher the note is positioned the
higher the pitch; the lower – the more “bass”.

In order to
distinguish sounds of different lengths we write notes with black or
white heads with all kinds of stems. Not all combinations are
allowed: for example there is no such symbol as a white note head
with a “flag” on its stem. The set of used symbols is as follows:

Depending on the length (duration) of a sound, we mark it with one of the symbols above

From left: the longest possible note is a whole note (white note head without a stem). Next:
a half note has half the length of a whole note.
A quarter note is – unsurprisingly – four times shorter than a whole note. Then we have the eighth,
sixteenth, and the thirty-second notes.

The direction of a note's stem, whether it is
going upwards or downwards, is not significant. It is only a
matter of aesthetics. Similarly the flags of neighboring eighth,
sixteenth, and thirty-second notes can be connected – it is also a
matter of aestethics (and convenience, meaning the ease
of drawing).

In our drawing every subsequent note stands for a
pitch lasting half as long as the previous one. Just like
digits in the binary system. If we need a note of “intermediate”
length we can follow one of the two procedures:

Add a dot behind the note. The dot increases the duration of a sound by 50%.

Connect the two notes with a tie. The tie combines the notes.

Example: eight sixteenth notes last the span of a
half note. Four thirty-second notes last just as long
as an eighth note. The length of three sixteenth notes is equal to
one eighth note with a dot. Two half notes connected by
a tie are a whole note.

Sometimes there is a rest (pause) in a melody.
Because silence does not have a frequency, pauses are always
positioned in the middle of the staff. The lengths of rests are built
similarly to the lengths of notes (i.e. “binarily”).

Symbols of rests of different durations

Right now, theoretically, we would be able to note
the rhythm of a piece, which would be enough to compose the
African-fire-percussion-music. However if we want to write a melody,
we have to learn the mapping of subsequent lines in the staff onto
specific frequencies. The pitches we have already learned and named,
meaning: C, D, E, F, G, A and B have their own, individually marked
spots:

The placement
of subsequent pitches, CDEFGABC, on the staff. Notice that we have connected the
“flags” of the eighth notes for aesthetic purposes.

We have also snuck in a new symbol, meaning the
treble clef
(clef means key in French). The clef's job is to
“calibrate” the staff, i.e. define the mapping between the
placement of a note and the frequency of the tone. There are also
other clefs, such as bass clef and tenor clef, which signal other
mappings. Don't worry about it now – all the songs in Temptonik
will be noted in treble clef.

Interlude: how to draw the clef?

The clef

After the clef another new symbol appears: meter.
Every musical piece is divided into segments called bars (or
measures), which include notes and pauses of strictly defined total
duration; these segments are separated by vertical lines (bar
lines). The meter defines how many quarter notes (or eighths) are
in each one of those bars. A number of songs are written in the 4/4
meter, meaning that four (top number) quarter notes (bottom number)
fit in each bar. A 7/8 meter would indicate that seven eighth notes
fit in one bar, and so on.

Pieces are divided into bars just like poems are
divided into verses. It puts their general structure in order (and
that is all). Meters other than 4/4 are uncommon in contemporary
popular music. Some popular exceptions are all kinds of waltzes
(3/4), “Nothing Else Matters” by Metallica (6/8),
“The Crunge” by Led Zeppelin (9/8)
or Mike Oldfield's
“Tubular Bells”
(15/8).
Sometimes there are also meter changes which take place during the
piece, like in the “Bohemian Rhapsody” by Queen.

Black keys on the piano don't have their spots on the
staff. Then how can we get to them? There are two ways to do this:

by raising the chosen
pitch (white key) by a semitone,

by lowering the chosen pitch (white key) by a
semitone.

How to note the raising of a pitch by a semitone? To
do this we have to use the sharp symbol.

The effects
of the sharp symbol. Notice that the sharp placed by the C note is
active until the end and regardless of the octave. We will explain
that in a moment.

In order to lower the pitch by a semitone we use the flat symbol.

The way flats
affect notes. Notice that the flat placed by the C note is active
until the end of the bar and acts regardless of the octave.

When to use the sharp and when the flat? Here the
concept of enharmonic comes bouncing back like a boomerang... and
that is why right now we are not going to bother with it. Both ways
have an equivalent final outcome, but usually one of them is
considered to be “more correct” (but there are also situations
when it's hard to determine this).

We should note that lowering and raising by a
semitone won't always lead us to a black key. Raising the E tone by a
semitone will result in E♯,
meaning... F. Similarly, F with a flat (F♭) will give us E. B with a sharp (B♯)
is C, and C with a flat (C♭) is just B. Pointless redundancy? Not really – we will delve into
this problem while discussing musical scales.

The sharp and the flat are the so-called chromatic
signs. Once a chromatic symbol
is placed it remains in effect on that one pitch for the
rest of the bar, which
beginners often tend to forget.

What should you do when you place the sharp or the
flat and you want to use “unmodified” pitch before the bar is
over? Use the natural:

The way naturals affect notes

A little too fast? Don't worry; we have discussed
almost everything we'll need. There are of course many details and
new symbols ahead of us, but we can provocatively say that those
details are secondary. We suggest that you – after this small jab
at theory – continue getting to know notes through examples, that
is, by studying your favorite songs at Temptonik.

Anyway, notes are
just a protocol of communication. In order to create and perform nice
tunes we have to get back to learning harmony, which we will dedicate
our next lessons to.

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